Evaluation of fundamental hypotheses underlying constrained mixture models of arterial growth and remodelling

Valentín, Arturo; Humphrey, Jay D.

doi:10.1098/rsta.2009.0113

Cited by 94 publications

(130 citation statements)

References 64 publications

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“…In this paper, we suggested yet another form of the stored energy function (equation (2.1)), one motivated directly by microstructural information on arterial collagen obtained using multi-photon microscopy [9], by excellent prior fits to data from diverse arteries [10,11,17], by new interpretive value related to residual and pre-stresses [12] and by utility in growth and remodelling theories [13,42]. We submit that this functional form fits available human biaxial data as well as or better than prior models (e.g.…”

Section: ð4:2þmentioning

confidence: 99%

“…Towards that end, we employ a 'four-fibre family' constitutive relation that is motivated by microscopic data on the organization of arterial collagen [9] and that captures differences in the mechanical behaviour of carotid arteries that result from diverse structural abnormalities in genetically modified mice [10,11], provides new insight into origins of residual stress and axial prestretch [12], and describes growth and remodelling in response to altered haemodynamics [13]. Moreover, we show that combining the technique for statistical inference known as non-parametric bootstrap with a modal clustering method yields improved confidence intervals for best-fit values of the model parameters, particularly given the possible non-uniqueness in nonlinear estimations.…”

Section: Introductionmentioning

confidence: 99%

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On constitutive descriptors of the biaxial mechanical behaviour of human abdominal aorta and aneurysms

Ferruzzi

Vorp

Humphrey

2010

J. R. Soc. Interface.

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165

159

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The abdominal aorta (AA) in older individuals can develop an aneurysm, which is of increasing concern in our ageing population. The structural integrity of the ageing aortic wall, and hence aneurysm, depends primarily on effective elastin and multiple families of oriented collagen fibres. In this paper, we show that a structurally motivated phenomenological 'fourfibre family' constitutive relation captures the biaxial mechanical behaviour of both the human AA, from ages less than 30 to over 60, and abdominal aortic aneurysms. Moreover, combining the statistical technique known as non-parametric bootstrap with a modal clustering method provides improved confidence intervals for estimated best-fit values of the eight associated constitutive parameters. It is suggested that this constitutive relation captures the well-known loss of structural integrity of elastic fibres owing to ageing and the development of abdominal aneurysms, and that it provides important insight needed to construct growth and remodelling models for aneurysms, which in turn promise to improve our ability to predict disease progression.

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Section: ð4:2þmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On constitutive descriptors of the biaxial mechanical behaviour of human abdominal aorta and aneurysms

Ferruzzi

Vorp

Humphrey

2010

J. R. Soc. Interface.

Self Cite

165

159

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“…stress-free) configuration, i.e. new constituents appear to be incorporated within extant matrix having a preferred prestress (Valentín & Humphrey, 2009a;Wagenseil & Mecham, 2007). We assume that such constituents are subsequently constrained to deform with the mixture (i.e.…”

Section: A Multiple Timescales Approachmentioning

confidence: 99%

Modelling carotid artery adaptations to dynamic alterations in pressure and flow over the cardiac cycle

Cardamone

Valentín

Eberth

et al. 2010

Mathematical Medicine and Biology

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Motivated by recent clinical and laboratory findings of important effects of pulsatile pressure and flow on arterial adaptations, we employ and extend an established constrained mixture framework of growth (change in mass) and remodelling (change in structure) to include such dynamical effects. New descriptors of cell and tissue behavior (constitutive relations) are postulated and refined based on new experimental data from a transverse aortic arch banding model in the mouse that increases pulsatile pressure and flow in one carotid artery. In particular, it is shown that there was a need to refine constitutive relations for the active stress generated by smooth muscle, to include both stress-and stress rate-mediated control of the turnover of cells and matrix and to account for a cyclic stress-mediated loss of elastic fibre integrity and decrease in collagen stiffness in order to capture the reported evolution, over 8 weeks, of luminal radius, wall thickness, axial force and in vivo axial stretch of the hypertensive mouse carotid artery. We submit, therefore, that complex aspects of adaptation by elastic arteries can be predicted by constrained mixture models wherein individual constituents are produced or removed at individual rates and to individual extents depending on changes in both stress and stress rate from normal values.

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“…In the derivation of the thin-walled tube theory we used CMT to derive the equilibrium equation for a thin-walled tube. CMT assumes that the vessel wall constituents deform together, and therefore undergo the same deformation [21,22,27,28]. The materials of tissues in the body are produced and degraded continually.…”

Section: Constrained Mixture Theorymentioning

confidence: 99%

“…Humphrey and co-workers have formulated an evolution equation for mass fractions by letting the mass production in the vessel wall depend on differences between actual and target homeostatic stresses [18,19,20,21,22]. The mechanical model used in their works is based on constrained mixture theory (CMT), which takes care of production and removal of arterial constituents.…”

Section: Motivationmentioning

confidence: 99%

Goal Function Approach to Growth and Remodeling of Arteries

Satha¹

2014

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In this thesis we develop a new goal function approach to investigate stability of the growth processes in blood vessels and cost-optimal composition and geometry of these vessels. In the vascular system of a healthy individual, the living composition of the arterial wall must regenerate and remodel continuously during the entire lifetime to maintain itself. In some cases the system destabilizes due to disease, injury or other complex processes. To understand how and when this happens, several mathematical models have been developed. These models have included an evolution equation for mass fractions of the vessel wall, describing how the vessel develops from an actual state to a target state. These works are based on constrained mixture theory (CMT), which takes care of production and removal of arterial constituents. The cost-optimal design of blood vessels has been studied previously by Murray. The aim of this thesis is to contribute to stability analyses of the growth process by formulating a new goal function approach, making it possible to examine under which conditions instability arises. We also aim to analyze changes in the optimum material composition and geometry of the vessel wall, using a more realistic, nonlinear material model. The blood vessel is modeled as a thin-walled tube and the constituents that form the vessel wall are assumed to deform together (CMT). The growth dynamics of the composite material of the vessel wall is described by an evolution equation, where the effective area of each constituent changes in the direction of steepest descent of a goal function. This goal function is formulated in such way that the constituents grow toward a target potential energy and a target composition. The response of the evolution equation is simulated for several dierent material models. These simulations suggest that elastin-decient vessels are more prone to growth instability, but that increased vessel stiness gives a more stable growth process. Another important nding is that an increased rate of degradation of materials impairs growth stability. By extending Murray's law to include effects of nonlinear mechanics of the artery wall and a growth and remodeling mechanism based on CMT, and at the same time having the system satisfy an equilibrium equation, we study cost-optimal compositions and geometries of the vessel wall. This gives new insight into the wall's architecture under optimal conditions

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Evaluation of fundamental hypotheses underlying constrained mixture models of arterial growth and remodelling

Cited by 94 publications

References 64 publications

On constitutive descriptors of the biaxial mechanical behaviour of human abdominal aorta and aneurysms

On constitutive descriptors of the biaxial mechanical behaviour of human abdominal aorta and aneurysms

Modelling carotid artery adaptations to dynamic alterations in pressure and flow over the cardiac cycle

Goal Function Approach to Growth and Remodeling of Arteries

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